Thermodynamic Stability of Schwarzschild-de Sitter Black holes with Rényi entropy

Abstract

Even though, classically, a black holes is gravitational object, it can be treated as a thermodynamic object when quantum effect is taken into account. It is found that by using Gibbs-Boltzmann entropy, thermodynamic system associated Schwarzschild-de Sitter black hole is unstable while it is stable under description of Rényi entropy. According to Rényi entropy, the thermodynamic phase space needed to be extended. Specifically, the non-extensive parameter must be treated as a thermodynamic variable. In this work, we investigate the thermodynamic stability of Schwarzschild-de Sitter black hole with Rényi entropy by treating non-extensive parameter as chemical potential. We found that it is possible to obtain the stability of the black hole under the process with fixing pressure, temperature and number of particles. We also found that there exist the phase transitions from the hot gas to the stable black hole in such the process. Therefore, if such a black hole is possibly observed, the non-extensive effect of Rényi statistics may provide a physical insight beyond the standard approach to black hole thermodynamics.